Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-4y &= 7 \\ -2x-4y &= 1\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-4y = 2x+1$ Divide both sides by $-4$ to isolate $y$ $y = {-\dfrac{1}{2}x - \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $-5x-4({-\dfrac{1}{2}x - \dfrac{1}{4}}) = 7$ $-5x + 2x + 1 = 7$ Simplify by combining terms, then solve for $x$ $-3x + 1 = 7$ $-3x = 6$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $-5( -2)-4y = 7$ $10-4y = 7$ $-4y = -3$ $y = \dfrac{3}{4}$ The solution is $\enspace x = -2, \enspace y = \dfrac{3}{4}$.